A limitation of the quantities derived from the MTP is that at gap
closure information about system size scaling is lost. The variance
of the polarization, as derived by Resta, diverges at gap closure,
even for finite systems. For this reason, techniques based on the
finite size scaling hypothesis [1]}, [2]} are not
directly applicable to metal-insulator transitions. Application of
the Binder cumulant technique [3]}, [4]} (based on the
finite size scaling hypothesis) in MTP is difficult for two reasons:
other than the loss of size scaling information already mentioned, a
Binder cumulant is a ratio of averages of expectation values of
observables (the order parameter), and in MTP the basic quantity is a
geometric phase, rather than the expectation value of an observable.
In this work we overcome both of these obstacles.
